XU Ji-qing, LI Zheng-liang, WU Lin-jian. A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function[J]. Applied Mathematics and Mechanics, 2014, 35(5): 533-541. doi: 10.3879/j.issn.1000-0887.2014.05.007
 Citation: XU Ji-qing, LI Zheng-liang, WU Lin-jian. A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function[J]. Applied Mathematics and Mechanics, 2014, 35(5): 533-541.

# A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function

##### doi: 10.3879/j.issn.1000-0887.2014.05.007
• Rev Recd Date: 2014-04-08
• Publish Date: 2014-05-15
• A new numerical calculation method for structural dynamic responses was proposed based on the approximation theory of radial basis function (RBF) and weighted residual collocation point method, with the time interval to replace the space distance as the independent variable of RBF for the first time. Aimed at the numerical characteristics of structural dynamics, a new RBF expression of joint interpolation combining displacement, velocity and acceleration was developed, and the concept and standard for precise calculation put forward. According to the numerical examples, the new method has significant advantages in solving strong stiff dynamic equations and structural transient-phase dynamic responses, compared with the Newmark method, Wilson-θ method and Runge-Kutta method. Its calculation accuracy is equivalent to that of the precise time-integration method. This new calculation method is independent of the computation efficiency-related dynamic eigen-matrix and the degrees of freedom of a problem. It has good applicability to some large-scale problems, and makes a promising way to the calculation of structural dynamic responses.
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